Cut all 12 rolls in half. Place the roll bottoms in a 9- by 13-inch pan. Place equal amounts of ham (about 3 slices) on each roll. Top with the gruyere. Spread a generous amount of the chive and cream cheese on the roll tops. Place the tops on top of each sandwich bottom.

Pour the butter mixture over the top of the sandwiches. Cover with foil and bake until the cheese is melted, about 20 minutes. Then remove the foil and bake an additional 5 minutes to toast the buns.

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